Questions we are exploring

Do floral traits vary across populations?

If floral traits vary across populations, are patterns of variation clinal, associated with variation in pollinators, or random?

In this file:

I provide a list of potential variables/approaches to consider to address the questions above. I then provide the results of most of these analyses, with the caveat that results may shift slightly after we account for response factors in the scent emission data and potentially clean up some erroneous values in the morphology data.

Floral traits that could vary

Overall approach: I think we are investigating whether differences between populations occur in floral morphology, floral scent, or a combination of the two.

(To facilitate our analyses, we reduced the number of floral scent variables under investigation by combining correlated compounds that are produced via the same biosynthetic pathways. I will make a supplement/appendix for the paper that shows how we did that.)

So, we can start with multivariate approaches that use the morphology variables, the scent variables, or both, and see how much of the total variance those approaches explain.

Then, we can unpack which variables in particular are different across populations.

Total emission rate and compound diversity are two variables that are essentially summaries of the whole scent dataset, so they won’t be included in the multivariate analyses, but will be analyzed regardless of the outcomes of the multivariate analyses.

Trait Approach
Floral scent, total emission rate Linear mixed model analysis across populations of total emission rates in toluene equivalents
Floral scent, compound diversity Linear mixed model analysis of the number of compounds in samples across populations
Floral scent, blend composition Multivariate analysis (e.g. Adonis) plus constrained ordination. Currently using emission rates in toluene equivalents, will ultimately convert this to emission rates adjusted for response factors.
We are doing this using emission rates that are the sums of all compounds produced from a certain biosynthetic cluster/table.
Floral scent, emission rates of key compounds or compound groups 1. identify what the key compound(s)/compound group(s) are from the constrained ordination.
2. linear mixed model analysis to compare across populations.
Floral morphology Multivariate analysis (e.g. Adonis) plus constrained ordination, followed by univariate mixed model analyses of key variables.
Scent & morphology together Multivariate analysis (e.g. Adonis) plus constrained ordination

Total emission rate

This is total emission rate (per g fresh mass) as a function of population, with plant nested within population as a random effect. So this makes use of all measured flowers.

Diagnostics for the model residuals:

Model summary:

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Comp.Total ~ Population + (1 | Pop_Plant)
##    Data: ER_f_mass
## 
## REML criterion at convergence: 3212.1
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
## -2.136 -0.371 -0.090  0.212  3.212 
## 
## Random effects:
##  Groups    Name        Variance Std.Dev.
##  Pop_Plant (Intercept) 41488296 6441    
##  Residual              44481777 6669    
## Number of obs: 157, groups:  Pop_Plant, 72
## 
## Fixed effects:
##                   Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)        5936.19    1790.52    62.93   3.315 0.001522 ** 
## PopulationZion     5465.22    3387.55    75.10   1.613 0.110869    
## PopulationInyo    10785.17    2829.70    69.39   3.811 0.000296 ***
## PopulationArizona  8772.25    2353.84    59.75   3.727 0.000433 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) PpltnZ PpltnI
## PopulatinZn -0.529              
## PopulatnIny -0.633  0.334       
## PopultnArzn -0.761  0.402  0.481

ANOVA:

## Type III Analysis of Variance Table with Satterthwaite's method
##               Sum Sq   Mean Sq NumDF  DenDF F value    Pr(>F)    
## Population 857042809 285680936     3 68.624  6.4224 0.0006734 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Estimated marginal means & contrasts across populations:

## $emmeans
##  Population emmean   SE   df lower.CL upper.CL
##  Logan        5936 1795 64.2     2351     9522
##  Zion        11401 2878 81.8     5675    17128
##  Inyo        16721 2195 75.5    12350    21093
##  Arizona     14708 1531 56.9    11642    17775
## 
## Degrees-of-freedom method: kenward-roger 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast        estimate   SE   df t.ratio p.value
##  Logan - Zion       -5465 3392 76.5 -1.611  0.3785 
##  Logan - Inyo      -10785 2835 70.7 -3.804  0.0017 
##  Logan - Arizona    -8772 2359 61.0 -3.718  0.0024 
##  Zion - Inyo        -5320 3620 79.4 -1.470  0.4604 
##  Zion - Arizona     -3307 3260 75.5 -1.014  0.7416 
##  Inyo - Arizona      2013 2676 68.8  0.752  0.8754 
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: tukey method for comparing a family of 4 estimates

Interpretation: total scent shows a roughly clinal pattern. Due to the amount of variance, the significant contrasts are that Logan has lower total scent than Inyo or Arizona. Zion is intermediate.

Compound diversity

This is the number of compounds detected in a sample as a function of population, with plant nested within population as a random effect. So this makes use of all measured flowers.

Diagnostics for the model residuals:

Model summary:

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Total ~ Population + (1 | Pop_Plant)
##    Data: P_A_totals
## 
## REML criterion at convergence: 854.8
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.59687 -0.51638  0.09328  0.60457  1.60926 
## 
## Random effects:
##  Groups    Name        Variance Std.Dev.
##  Pop_Plant (Intercept) 10.342   3.216   
##  Residual               9.245   3.040   
## Number of obs: 155, groups:  Pop_Plant, 72
## 
## Fixed effects:
##                   Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)        12.9716     0.8775 64.7604  14.782  < 2e-16 ***
## PopulationZion      2.7123     1.6382 73.2571   1.656  0.10206    
## PopulationInyo      4.6145     1.3733 68.7880   3.360  0.00127 ** 
## PopulationArizona   3.2289     1.1495 60.7459   2.809  0.00668 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) PpltnZ PpltnI
## PopulatinZn -0.536              
## PopulatnIny -0.639  0.342       
## PopultnArzn -0.763  0.409  0.488

ANOVA:

## Type III Analysis of Variance Table with Satterthwaite's method
##            Sum Sq Mean Sq NumDF  DenDF F value   Pr(>F)   
## Population 121.18  40.395     3 67.738  4.3695 0.007147 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Estimated marginal means & contrasts across populations:

## $emmeans
##  Population emmean    SE   df lower.CL upper.CL
##  Logan        13.0 0.880 66.8     11.2     14.7
##  Zion         15.7 1.384 79.0     12.9     18.4
##  Inyo         17.6 1.058 73.8     15.5     19.7
##  Arizona      16.2 0.744 57.5     14.7     17.7
## 
## Degrees-of-freedom method: kenward-roger 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast        estimate   SE   df t.ratio p.value
##  Logan - Zion      -2.712 1.64 75.3 -1.654  0.3554 
##  Logan - Inyo      -4.614 1.38 70.8 -3.354  0.0069 
##  Logan - Arizona   -3.229 1.15 62.7 -2.803  0.0332 
##  Zion - Inyo       -1.902 1.74 77.1 -1.092  0.6956 
##  Zion - Arizona    -0.517 1.57 73.6 -0.329  0.9876 
##  Inyo - Arizona     1.386 1.29 67.9  1.072  0.7079 
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: tukey method for comparing a family of 4 estimates

Interpretation: The total number of compounds also shows a clinal pattern. The significant contrasts are that Logan has fewer compounds than Inyo and Arizona.

Floral scent blend composition, multivariate analyses using groupings by biosynthetic pathway

Note: these results could change once we are working with emission rates adjusted for response factors

These are the groupings of the compounds (ver. 2.0):

Code Compounds
G.ILE 2 methylbuyronitrile, nitro-2-methyl butane, cis-2-methylbutyraldoxime, trans-2-methylbutyraldoxime
G.LEU 3methylbutyronitrile, nitro-3-methyl-butane, cis-3-methylbutyraldoxime, trans-3-methylbutyraldoxime, cis-isobutyraldoxime, trans-isobutyraldoxime
G.PHE 2phenylethanol, phenylacetonitrile, nitrophenylethane, phenylacetaldoxime
G.OCI b-myrcene, cis-b-ocimene, trans-b-ocimene
G.GER citronellol, neral, geranial, nerol, geraniol
G.LIN linalool
G.LOX cis-furanoid-linalool-oxide, trans-furanoid-linalool-oxide, pyran-lin-oxide-ketone, cis-pyranoid-linalool-oxide, trans-pyranoid-linalool-oxide
G.CAR beta-caryophyllene, alpha-humulene, caryophyllene-oxide, farnesol
G.NER nerolidol
G.ISO isophytol
G.ALT alpha-terpineol
G.FAR beta-farnesene, Z-E-alpha-farnesene, E-E-alpha-farnesene, farnesene-epoxide

First, running an adonis (comparable to ANOSIM):

## 
## Call:
## adonis(formula = ER_f_mass_group_data ~ Population, data = ER_f_mass_groups,      permutations = 999, method = "bray") 
## 
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##            Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)    
## Population  3    3.4156 1.13853  6.2947 0.22512  0.001 ***
## Residuals  65   11.7567 0.18087         0.77488           
## Total      68   15.1723                 1.00000           
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Interpretation: The adonis shows a significant effect of population, which explains about 23 % of the variance in scent blend composition.

Running a constrained analysis of principle coordinates:

## 
## Call:
## capscale(formula = ER_f_mass_group_data ~ Population, data = ER_f_mass_groups,      distance = "bray") 
## 
## Partitioning of squared Bray distance:
##               Inertia Proportion
## Total          16.979     1.0000
## Constrained     3.499     0.2061
## Unconstrained  13.481     0.7939
## 
## Eigenvalues, and their contribution to the squared Bray distance 
## 
## Importance of components:
##                         CAP1     CAP2     CAP3   MDS1   MDS2   MDS3    MDS4
## Eigenvalue            3.2414 0.130950 0.126292 3.1226 2.3205 1.7721 1.25862
## Proportion Explained  0.1909 0.007712 0.007438 0.1839 0.1367 0.1044 0.07413
## Cumulative Proportion 0.1909 0.198617 0.206055 0.3900 0.5266 0.6310 0.70512
##                          MDS5   MDS6   MDS7    MDS8    MDS9   MDS10   MDS11
## Eigenvalue            0.95712 0.7692 0.5960 0.52174 0.36536 0.28894 0.25091
## Proportion Explained  0.05637 0.0453 0.0351 0.03073 0.02152 0.01702 0.01478
## Cumulative Proportion 0.76149 0.8068 0.8419 0.87263 0.89414 0.91116 0.92594
##                         MDS12   MDS13   MDS14    MDS15    MDS16    MDS17
## Eigenvalue            0.20075 0.18159 0.17264 0.129959 0.103850 0.088593
## Proportion Explained  0.01182 0.01069 0.01017 0.007654 0.006116 0.005218
## Cumulative Proportion 0.93776 0.94846 0.95863 0.966279 0.972396 0.977613
##                         MDS18   MDS19    MDS20    MDS21    MDS22   MDS23
## Eigenvalue            0.07979 0.06487 0.044465 0.043061 0.037929 0.02649
## Proportion Explained  0.00470 0.00382 0.002619 0.002536 0.002234 0.00156
## Cumulative Proportion 0.98231 0.98613 0.988752 0.991288 0.993522 0.99508
##                          MDS24     MDS25     MDS26     MDS27     MDS28
## Eigenvalue            0.023999 0.0169519 0.0165729 0.0115865 0.0058020
## Proportion Explained  0.001413 0.0009984 0.0009761 0.0006824 0.0003417
## Cumulative Proportion 0.996496 0.9974939 0.9984700 0.9991524 0.9994941
##                           MDS29    MDS30    MDS31     MDS32
## Eigenvalue            0.0031433 0.002802 0.002479 1.647e-04
## Proportion Explained  0.0001851 0.000165 0.000146 9.697e-06
## Cumulative Proportion 0.9996792 0.999844 0.999990 1.000e+00
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CAP1    CAP2   CAP3
## Eigenvalue            3.2414 0.13095 0.1263
## Proportion Explained  0.9265 0.03743 0.0361
## Cumulative Proportion 0.9265 0.96390 1.0000
## 
## Scaling 2 for species and site scores
## * Species are scaled proportional to eigenvalues
## * Sites are unscaled: weighted dispersion equal on all dimensions
## * General scaling constant of scores:

The constrained portion explains about 21% of overall distance. CAP1 explains about 19% and CAP2 expalins about 1% of overall distance. I suggest this means we should really be looking at the compounds that are correlated with CAP1

Plotting the capscale:

Checking to see which compound group(s) are significantly correlated with CAP1 and/or CAP2.

compounds cor1 p1 cor2 p2 sig1 sig2
G.ILE 0.4839 0.0001 -0.2587 0.0792 Yes No
G.LEU 0.5139 0.0000 0.2571 0.0792 Yes No
G.PHE -0.1889 0.2057 0.1049 0.4699 No No
G.OCI -0.0091 0.9409 0.54 0.0000 No Yes
G.GER 0.1506 0.2603 -0.1048 0.4699 No No
G.LIN 0.6951 0.0000 0.0645 0.6527 Yes No
G.LOX -0.1395 0.2761 -0.2897 0.0630 No No
G.CAR -0.2239 0.1287 -0.1054 0.4699 No No
G.FAR -0.1681 0.2232 0.4281 0.0015 No Yes
G.NER -0.1684 0.2232 -0.0425 0.7291 No No
G.ISO 0.2682 0.0621 0.1536 0.3562 No No
G.ALT 0.3538 0.0086 0.1726 0.3124 Yes No

This table indicates that six compound groups are correlated with CAP1 at P adjusted < 0.01 : ILE, LEU, LIN, ALT. Two compound groups are correlated with CAP2: OCI, FAR.

Floral scent, univariate analyses of key compound groups

Note: these results could change once we are working with emission rates adjusted for response factors. Also will need to check for p-value adjustments for performing mulitple tests (e.g. one test for each compound group).

For each compound group that was correlated with CAP1 and/or CAP2, the emission rate is modeled as a function of population, with plant nested within population as a random effect. This uses data from all measured flowers.

ER_f_mass_groups <- ER_f_mass %>% mutate(G.ILE=Comp.2methylbutyronitrile+`Comp.nitro-2-methyl-butane`+`Comp.cis-2-methylbutyraldoxime`+`Comp.trans-2-methylbutyraldoxime`,
                                         G.LEU=Comp.3methylbutyronitrile+`Comp.nitro-3-methyl-butane`+`Comp.cis-3-methylbutyraldoxime`+`Comp.trans-3-methylbutyraldoxime`+`Comp.cis-isobutyraldoxime`+`Comp.trans-isobutyraldoxime`,
                                        
                                         G.PHE=Comp.2phenylethanol+Comp.phenylacetonitrile+Comp.nitrophenylethane+Comp.phenylacetaldoxime,
                                         G.OCI=`Comp.b-myrcene`+`Comp.cis-b-ocimene`+`Comp.trans-b-ocimene`,
                                         G.GER=Comp.citronellol+Comp.neral+Comp.geranial+Comp.nerol+Comp.geraniol,
                                         G.LIN=Comp.linalool,
                                         G.LOX=`Comp.cis-furanoid-linalool-oxide`+`Comp.trans-furanoid-linalool-oxide`+`Comp.pyran-lin-oxide-ketone`+`Comp.cis-pyranoid-linalool-oxide`+`Comp.trans-pyranoid-linalool-oxide`,
                                         G.CAR=`Comp.beta-caryophyllene`+`Comp.alpha-humulene`+`Comp.caryophyllene-oxide`+Comp.farnesol,
                                         G.FAR=`Comp.beta-farnesene`+`Comp.Z-E-alpha-farnesene`+`Comp.E-E-alpha-farnesene`+`Comp.farnesene-epoxide`,
                                         G.SES=Comp.nerolidol+Comp.isophytol,
                                         G.NER=Comp.nerolidol,
                                         G.ISO=Comp.isophytol,
                                         G.ALT=`Comp.alpha-terpineol`)

ER_f_mass_group_data <- ER_f_mass_groups %>% select(starts_with("G."))

ER_f_mass_group_data <- ER_f_mass_group_data %>% slice(.,-c(36,44))
ER_f_mass_groups <- ER_f_mass_groups %>% slice(.,-c(36,44))

ILE group:

Diagnostics for the model residuals:

Model summary:

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: G.ILE ~ Population + (1 | Pop_Plant)
##    Data: ER_f_mass_groups
## 
## REML criterion at convergence: 2664.7
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.2608 -0.4180 -0.1058  0.2763  3.2117 
## 
## Random effects:
##  Groups    Name        Variance Std.Dev.
##  Pop_Plant (Intercept) 2028620  1424    
##  Residual              1358393  1166    
## Number of obs: 155, groups:  Pop_Plant, 72
## 
## Fixed effects:
##                   Estimate Std. Error      df t value Pr(>|t|)   
## (Intercept)         624.99     371.84   70.60   1.681  0.09722 . 
## PopulationZion     1539.41     690.55   76.90   2.229  0.02872 * 
## PopulationInyo      834.59     580.45   73.55   1.438  0.15472   
## PopulationArizona  1463.53     488.52   67.01   2.996  0.00383 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) PpltnZ PpltnI
## PopulatinZn -0.538              
## PopulatnIny -0.641  0.345       
## PopultnArzn -0.761  0.410  0.488

ANOVA:

## Type III Analysis of Variance Table with Satterthwaite's method
##              Sum Sq Mean Sq NumDF  DenDF F value  Pr(>F)  
## Population 13900701 4633567     3 72.587  3.4111 0.02191 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Estimated marginal means & contrasts across populations:

## $emmeans
##  Population emmean  SE   df lower.CL upper.CL
##  Logan         625 372 67.7     -118     1368
##  Zion         2164 582 76.7     1005     3324
##  Inyo         1460 446 72.8      570     2349
##  Arizona      2089 317 59.6     1454     2723
## 
## Degrees-of-freedom method: kenward-roger 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast        estimate  SE   df t.ratio p.value
##  Logan - Zion     -1539.4 691 74.0 -2.227  0.1254 
##  Logan - Inyo      -834.6 581 70.6 -1.436  0.4814 
##  Logan - Arizona  -1463.5 489 64.2 -2.992  0.0200 
##  Zion - Inyo        704.8 733 75.2  0.961  0.7719 
##  Zion - Arizona      75.9 663 72.4  0.114  0.9995 
##  Inyo - Arizona    -628.9 547 68.0 -1.149  0.6607 
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: tukey method for comparing a family of 4 estimates

Interpretation: Arizona has higher ILE emissions than Logan. All other contrasts are non-significant.

LEU group:

Diagnostics for the model residuals:

Untransformed residuals look okay, square root transformation (not shown) is comparable and doesn’t affect the results.

Model summary:

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: G.LEU ~ Population + (1 | Pop_Plant)
##    Data: ER_f_mass_groups
## 
## REML criterion at convergence: 2841.3
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.8229 -0.3741 -0.0457  0.2252  4.2610 
## 
## Random effects:
##  Groups    Name        Variance Std.Dev.
##  Pop_Plant (Intercept) 6125293  2475    
##  Residual              4507075  2123    
## Number of obs: 155, groups:  Pop_Plant, 72
## 
## Fixed effects:
##                   Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)         322.25     654.99   63.57   0.492 0.624422    
## PopulationZion     1933.11    1218.30   70.45   1.587 0.117052    
## PopulationInyo     4576.09    1023.23   66.80   4.472 3.08e-05 ***
## PopulationArizona  3140.07     859.72   59.91   3.652 0.000548 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) PpltnZ PpltnI
## PopulatinZn -0.538              
## PopulatnIny -0.640  0.344       
## PopultnArzn -0.762  0.410  0.488

ANOVA:

## Type III Analysis of Variance Table with Satterthwaite's method
##               Sum Sq  Mean Sq NumDF  DenDF F value    Pr(>F)    
## Population 103931007 34643669     3 65.815  7.6865 0.0001768 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Estimated marginal means & contrasts across populations:

## $emmeans
##  Population emmean   SE   df lower.CL upper.CL
##  Logan         322  656 67.4     -987     1632
##  Zion         2255 1028 77.4      209     4302
##  Inyo         4898  787 73.1     3330     6467
##  Arizona      3462  558 59.0     2346     4578
## 
## Degrees-of-freedom method: kenward-roger 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast        estimate   SE   df t.ratio p.value
##  Logan - Zion       -1933 1219 74.4 -1.585  0.3932 
##  Logan - Inyo       -4576 1025 70.7 -4.466  0.0002 
##  Logan - Arizona    -3140  861 63.7 -3.647  0.0029 
##  Zion - Inyo        -2643 1295 75.8 -2.042  0.1821 
##  Zion - Arizona     -1207 1169 72.8 -1.032  0.7312 
##  Inyo - Arizona      1436  964 68.0  1.489  0.4497 
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: tukey method for comparing a family of 4 estimates

Interpretation: Inyo and Arizona have higher emission rates of LEU compounds relative to Logan.

linalool:

Diagnostics for the model residuals:

Untransformed residuals look okay, square root transformation (not shown) is comparable and doesn’t affect the results.

Model summary:

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: G.LIN ~ Population + (1 | Pop_Plant)
##    Data: ER_f_mass_groups
## 
## REML criterion at convergence: 3004.3
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.9098 -0.3302 -0.0991  0.1478  3.5530 
## 
## Random effects:
##  Groups    Name        Variance Std.Dev.
##  Pop_Plant (Intercept)  9909569 3148    
##  Residual              16565500 4070    
## Number of obs: 155, groups:  Pop_Plant, 72
## 
## Fixed effects:
##                   Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)        2337.79     970.89   52.93   2.408   0.0196 *  
## PopulationZion     3479.35    1840.99   67.84   1.890   0.0630 .  
## PopulationInyo     7050.58    1531.40   60.04   4.604 2.20e-05 ***
## PopulationArizona  5678.78    1263.20   48.51   4.496 4.32e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) PpltnZ PpltnI
## PopulatinZn -0.527              
## PopulatnIny -0.634  0.334       
## PopultnArzn -0.769  0.405  0.487

ANOVA:

## Type III Analysis of Variance Table with Satterthwaite's method
##               Sum Sq   Mean Sq NumDF  DenDF F value    Pr(>F)    
## Population 464043699 154681233     3 58.846  9.3376 3.851e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Estimated marginal means & contrasts across populations:

## $emmeans
##  Population emmean   SE   df lower.CL upper.CL
##  Logan        2338  975 63.3      389     4287
##  Zion         5817 1566 85.7     2703     8931
##  Inyo         9388 1187 76.3     7024    11753
##  Arizona      8017  811 52.4     6389     9644
## 
## Degrees-of-freedom method: kenward-roger 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast        estimate   SE   df t.ratio p.value
##  Logan - Zion       -3479 1845 78.8 -1.886  0.2425 
##  Logan - Inyo       -7051 1537 70.8 -4.589  0.0001 
##  Logan - Arizona    -5679 1269 58.5 -4.477  0.0002 
##  Zion - Inyo        -3571 1965 82.2 -1.817  0.2727 
##  Zion - Arizona     -2199 1764 77.2 -1.247  0.5991 
##  Inyo - Arizona      1372 1438 67.6  0.954  0.7757 
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: tukey method for comparing a family of 4 estimates

Interpretation: Inyo and Arizona emit more linalool than Logan.

alpha terpineol:

Diagnostics for the model residuals:

Square-root transformation applied to improve residuals.

Model summary:

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(G.ALT) ~ Population + (1 | Pop_Plant)
##    Data: ER_f_mass_groups
## 
## REML criterion at convergence: 570.9
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.68791 -0.47838 -0.04125  0.63549  2.29612 
## 
## Random effects:
##  Groups    Name        Variance Std.Dev.
##  Pop_Plant (Intercept) 0.665    0.8155  
##  Residual              1.841    1.3570  
## Number of obs: 155, groups:  Pop_Plant, 72
## 
## Fixed effects:
##                   Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)        1.58687    0.28542 66.07693   5.560 5.24e-07 ***
## PopulationZion    -0.05045    0.55029 89.02134  -0.092   0.9272    
## PopulationInyo    -0.85800    0.45411 77.34429  -1.889   0.0626 .  
## PopulationArizona  1.81384    0.36943 61.05085   4.910 7.14e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) PpltnZ PpltnI
## PopulatinZn -0.519              
## PopulatnIny -0.629  0.326       
## PopultnArzn -0.773  0.401  0.486

ANOVA:

## Type III Analysis of Variance Table with Satterthwaite's method
##            Sum Sq Mean Sq NumDF  DenDF F value    Pr(>F)    
## Population  92.35  30.783     3 75.906  16.718 1.965e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Estimated marginal means & contrasts across populations:

## $emmeans
##  Population response    SE   df lower.CL upper.CL
##  Logan         2.518 0.912 59.2 1.023476     4.67
##  Zion          2.361 1.448 92.4 0.360621     6.11
##  Inyo          0.531 0.517 78.6 0.000543     2.06
##  Arizona      11.565 1.604 48.0 8.564666    15.01
## 
## Degrees-of-freedom method: kenward-roger 
## Confidence level used: 0.95 
## Intervals are back-transformed from the sqrt scale 
## 
## $contrasts
##  contrast        estimate    SE   df t.ratio p.value
##  Logan - Zion      0.0505 0.552 82.0  0.091  0.9997 
##  Logan - Inyo      0.8580 0.456 70.2  1.880  0.2459 
##  Logan - Arizona  -1.8138 0.372 54.3 -4.878  0.0001 
##  Zion - Inyo       0.8076 0.590 87.2  1.369  0.5218 
##  Zion - Arizona   -1.8643 0.527 81.0 -3.538  0.0037 
##  Inyo - Arizona   -2.6718 0.426 67.4 -6.276  <.0001 
## 
## Note: contrasts are still on the sqrt scale 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: tukey method for comparing a family of 4 estimates

Interpretation: Arizona has higher emission rates of alpha terpineol than all other populations.

FAR group–correlated with CAP2 only:

Diagnostics for the model residuals:

Model summary:

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: G.FAR ~ Population + (1 | Pop_Plant)
##    Data: ER_f_mass_groups
## 
## REML criterion at convergence: 2618.2
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -5.1113 -0.1234 -0.0005 -0.0001  5.0705 
## 
## Random effects:
##  Groups    Name        Variance Std.Dev.
##  Pop_Plant (Intercept) 2282509  1510.8  
##  Residual               797229   892.9  
## Number of obs: 155, groups:  Pop_Plant, 72
## 
## Fixed effects:
##                   Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)        1352.69     366.14    69.69   3.694 0.000435 ***
## PopulationZion    -1323.71     674.57    72.74  -1.962 0.053552 .  
## PopulationInyo     -470.98     569.43    71.06  -0.827 0.410944    
## PopulationArizona -1351.25     483.72    67.32  -2.793 0.006785 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) PpltnZ PpltnI
## PopulatinZn -0.543              
## PopulatnIny -0.643  0.349       
## PopultnArzn -0.757  0.411  0.487

ANOVA:

## Type III Analysis of Variance Table with Satterthwaite's method
##             Sum Sq Mean Sq NumDF  DenDF F value  Pr(>F)  
## Population 7355896 2451965     3 70.373  3.0756 0.03309 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Estimated marginal means & contrasts across populations:

## $emmeans
##  Population  emmean  SE   df lower.CL upper.CL
##  Logan      1352.69 366 68.6    621.8     2084
##  Zion         28.98 567 72.9  -1100.4     1158
##  Inyo        881.71 436 70.9     11.8     1752
##  Arizona       1.45 316 63.2   -630.5      633
## 
## Degrees-of-freedom method: kenward-roger 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast        estimate  SE   df t.ratio p.value
##  Logan - Zion      1323.7 675 71.6  1.962  0.2122 
##  Logan - Inyo       471.0 570 69.9  0.827  0.8416 
##  Logan - Arizona   1351.2 484 66.2  2.792  0.0337 
##  Zion - Inyo       -852.7 715 72.2 -1.192  0.6336 
##  Zion - Arizona      27.5 649 70.5  0.042  1.0000 
##  Inyo - Arizona     880.3 539 68.1  1.634  0.3669 
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: tukey method for comparing a family of 4 estimates

Interpretation: Logan emits more FAR compounds than Arizona.

OCI group–correlated with CAP2 only:

Diagnostics for the model residuals:

Model summary:

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: G.OCI ~ Population + (1 | Pop_Plant)
##    Data: ER_f_mass_groups
## 
## REML criterion at convergence: 2529.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.7155 -0.1261 -0.0546  0.0008  5.4062 
## 
## Random effects:
##  Groups    Name        Variance Std.Dev.
##  Pop_Plant (Intercept) 1812563  1346.3  
##  Residual               354429   595.3  
## Number of obs: 155, groups:  Pop_Plant, 72
## 
## Fixed effects:
##                   Estimate Std. Error      df t value Pr(>|t|)   
## (Intercept)         898.92     312.78   70.71   2.874  0.00535 **
## PopulationZion     -873.13     573.97   72.31  -1.521  0.13257   
## PopulationInyo     -887.43     485.58   71.40  -1.828  0.07179 . 
## PopulationArizona   -55.93     414.68   69.20  -0.135  0.89310   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) PpltnZ PpltnI
## PopulatinZn -0.545              
## PopulatnIny -0.644  0.351       
## PopultnArzn -0.754  0.411  0.486

ANOVA:

## Type III Analysis of Variance Table with Satterthwaite's method
##             Sum Sq Mean Sq NumDF  DenDF F value Pr(>F)
## Population 1998661  666220     3 70.946  1.8797 0.1408

No differences across populations.

Floral morphology, multivariate analyses

In order to do multivariate analyses of the morphological variables, I had to drop leaf number and leaf length, because there isn’t enough data.

## 
## Call:
## adonis(formula = morph_data ~ Population, data = morph_names,      permutations = 999, method = "bray") 
## 
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##            Df SumsOfSqs  MeanSqs F.Model      R2 Pr(>F)    
## Population  3   0.24907 0.083024  8.8739 0.38795  0.001 ***
## Residuals  42   0.39295 0.009356         0.61205           
## Total      45   0.64203                  1.00000           
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Interpretation: There is a significant effect of Population. It explains about 39 % of the variation in morphology.

Running a constrained analysis of principle coordinates:

## 
## Call:
## capscale(formula = morph_data ~ Population, data = morph_names,      distance = "bray") 
## 
## Partitioning of squared Bray distance:
##               Inertia Proportion
## Total          0.7698     1.0000
## Constrained    0.2544     0.3305
## Unconstrained  0.5154     0.6695
## 
## Eigenvalues, and their contribution to the squared Bray distance 
## 
## Importance of components:
##                         CAP1    CAP2     CAP3   MDS1    MDS2    MDS3    MDS4
## Eigenvalue            0.2042 0.04793 0.002334 0.2299 0.07166 0.04561 0.04071
## Proportion Explained  0.2652 0.06227 0.003032 0.2986 0.09308 0.05925 0.05289
## Cumulative Proportion 0.2652 0.32748 0.330511 0.6292 0.72224 0.78149 0.83438
##                          MDS5    MDS6    MDS7    MDS8    MDS9    MDS10    MDS11
## Eigenvalue            0.03430 0.02234 0.01351 0.01195 0.01082 0.007396 0.006189
## Proportion Explained  0.04456 0.02902 0.01755 0.01553 0.01406 0.009608 0.008040
## Cumulative Proportion 0.87894 0.90796 0.92551 0.94104 0.95510 0.964707 0.972747
##                          MDS12    MDS13    MDS14    MDS15    MDS16    MDS17
## Eigenvalue            0.005308 0.004060 0.003038 0.002506 0.001943 0.001320
## Proportion Explained  0.006895 0.005274 0.003946 0.003256 0.002525 0.001715
## Cumulative Proportion 0.979642 0.984917 0.988863 0.992119 0.994643 0.996358
##                          MDS18     MDS19     MDS20     MDS21     MDS22
## Eigenvalue            0.000988 0.0008716 0.0004951 0.0003749 7.392e-05
## Proportion Explained  0.001283 0.0011322 0.0006432 0.0004870 9.603e-05
## Cumulative Proportion 0.997642 0.9987738 0.9994170 0.9999040 1.000e+00
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CAP1    CAP2     CAP3
## Eigenvalue            0.2042 0.04793 0.002334
## Proportion Explained  0.8024 0.18840 0.009175
## Cumulative Proportion 0.8024 0.99083 1.000000
## 
## Scaling 2 for species and site scores
## * Species are scaled proportional to eigenvalues
## * Sites are unscaled: weighted dispersion equal on all dimensions
## * General scaling constant of scores:

The constrained portion explains about 33% of overall distance. CAP1 explains about 27% and CAP2 expalins about 6% of overall distance.

Plotting the capscale:

Checking to see which traits are significantly correlated with CAP1 and/or CAP2.

variables cor1 p1 cor2 p2 sig1 sig2
M.Corolla_D1 0.2619 0.0886 0.0846 0.6481 No No
M.Corolla_D2 0.7326 0.0000 0.3963 0.0144 Yes No
M.Tube_Flare 0.5669 0.0001 0.2913 0.0636 Yes No
M.Stamen_Length 0.669 0.0000 0.3271 0.0398 Yes No
M.Style_Length 0.5906 0.0000 0.4047 0.0144 Yes No
M.Hypanthium_Length 0.6229 0.0000 -0.5591 0.0002 Yes Yes
M.Pedicel_Length -0.2391 0.1096 0.5711 0.0002 No Yes
M.Nectar_Column 0.79 0.0000 -0.3636 0.0234 Yes No
M.Percent_Sugar 0.5667 0.0001 -0.0442 0.7704 Yes No

From this, all variables except for pedicel length and Corolla D1 are correlated with CAP1, and all of them are positively correlated.

The only variables correlated with CAP2 are hypanthium length (negative) and pedicel length (positive).

Floral morphology, univariate analyses

Looking at all nine floral morphology variables, as all were correlated with CAP1 and/or CAP2. Each variable is modeled as a function of population, with plant nested within population as a random effect. This uses data from all measured flowers where all variables were measured on the flower.

Corolla D2:

Diagnostics for the model residuals:

Model summary:

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: M.Corolla_D2 ~ Population + (1 | Pop_Plant)
##    Data: morph_names
## 
## REML criterion at convergence: 740.1
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.6251 -0.4669 -0.0388  0.4354  1.8214 
## 
## Random effects:
##  Groups    Name        Variance Std.Dev.
##  Pop_Plant (Intercept) 36.01    6.001   
##  Residual              23.67    4.865   
## Number of obs: 113, groups:  Pop_Plant, 63
## 
## Fixed effects:
##                   Estimate Std. Error     df t value Pr(>|t|)    
## (Intercept)         76.002      1.736 54.173  43.780  < 2e-16 ***
## PopulationZion      24.461      3.168 62.518   7.720 1.15e-10 ***
## PopulationInyo      14.396      2.678 58.110   5.375 1.42e-06 ***
## PopulationArizona    8.029      2.239 53.095   3.585 0.000732 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) PpltnZ PpltnI
## PopulatinZn -0.548              
## PopulatnIny -0.648  0.355       
## PopultnArzn -0.775  0.425  0.502

ANOVA:

## Type III Analysis of Variance Table with Satterthwaite's method
##            Sum Sq Mean Sq NumDF  DenDF F value    Pr(>F)    
## Population 1618.3  539.44     3 58.663  22.791 6.616e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Estimated marginal means & contrasts across populations:

## $emmeans
##  Population emmean   SE   df lower.CL upper.CL
##  Logan        76.0 1.74 56.3     72.5     79.5
##  Zion        100.5 2.65 68.5     95.2    105.8
##  Inyo         90.4 2.04 63.2     86.3     94.5
##  Arizona      84.0 1.42 53.6     81.2     86.9
## 
## Degrees-of-freedom method: kenward-roger 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast        estimate   SE   df t.ratio p.value
##  Logan - Zion      -24.46 3.17 64.6 -7.713  <.0001 
##  Logan - Inyo      -14.40 2.68 60.2 -5.369  <.0001 
##  Logan - Arizona    -8.03 2.24 55.2 -3.580  0.0039 
##  Zion - Inyo        10.07 3.35 66.5  3.007  0.0190 
##  Zion - Arizona     16.43 3.01 64.9  5.464  <.0001 
##  Inyo - Arizona      6.37 2.48 60.0  2.562  0.0607 
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: tukey method for comparing a family of 4 estimates

Interpretation: Zion has a significantly larger corolla dimension 2 relative to all other populations. Inyo and Arizona have the next largest corolla D2, which is larger than Logan.

Tube Flare:

Diagnostics for the model residuals:

Model summary:

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: M.Tube_Flare ~ Population + (1 | Pop_Plant)
##    Data: morph_names
## 
## REML criterion at convergence: 329
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.9872 -0.5545 -0.0399  0.5449  3.6777 
## 
## Random effects:
##  Groups    Name        Variance Std.Dev.
##  Pop_Plant (Intercept) 0.5596   0.748   
##  Residual              0.6676   0.817   
## Number of obs: 113, groups:  Pop_Plant, 63
## 
## Fixed effects:
##                   Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)         8.0467     0.2395 54.3746  33.591  < 2e-16 ***
## PopulationZion      1.9806     0.4446 67.3043   4.455 3.25e-05 ***
## PopulationInyo      1.0110     0.3726 60.4772   2.713  0.00866 ** 
## PopulationArizona   0.4937     0.3083 52.8497   1.601  0.11530    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) PpltnZ PpltnI
## PopulatinZn -0.539              
## PopulatnIny -0.643  0.346       
## PopultnArzn -0.777  0.419  0.499

ANOVA:

## Type III Analysis of Variance Table with Satterthwaite's method
##            Sum Sq Mean Sq NumDF  DenDF F value    Pr(>F)    
## Population 14.816  4.9388     3 61.085  7.3982 0.0002629 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Estimated marginal means & contrasts across populations:

## $emmeans
##  Population emmean    SE   df lower.CL upper.CL
##  Logan        8.05 0.240 54.2     7.56     8.53
##  Zion        10.03 0.375 73.1     9.28    10.77
##  Inyo         9.06 0.286 65.0     8.49     9.63
##  Arizona      8.54 0.195 50.5     8.15     8.93
## 
## Degrees-of-freedom method: kenward-roger 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast        estimate    SE   df t.ratio p.value
##  Logan - Zion      -1.981 0.445 67.2 -4.447  0.0002 
##  Logan - Inyo      -1.011 0.374 60.3 -2.707  0.0427 
##  Logan - Arizona   -0.494 0.309 52.7 -1.596  0.3896 
##  Zion - Inyo        0.970 0.472 70.0  2.056  0.1779 
##  Zion - Arizona     1.487 0.423 67.7  3.519  0.0042 
##  Inyo - Arizona     0.517 0.346 60.0  1.495  0.4467 
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: tukey method for comparing a family of 4 estimates

Interpretation: Zion is equal to Inyo, but greater than Arizona or Logan. Inyo is equal to Arizona, and greater than Logan. Arizona and Logan are equivalent.

Stamen Length:

Diagnostics for the model residuals:

Model summary:

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: M.Stamen_Length ~ Population + (1 | Pop_Plant)
##    Data: morph_names
## 
## REML criterion at convergence: 606.2
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.37343 -0.44195  0.01174  0.48588  2.92579 
## 
## Random effects:
##  Groups    Name        Variance Std.Dev.
##  Pop_Plant (Intercept) 7.989    2.826   
##  Residual              8.051    2.837   
## Number of obs: 113, groups:  Pop_Plant, 63
## 
## Fixed effects:
##                   Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)        23.8270     0.8763 55.4607  27.191  < 2e-16 ***
## PopulationZion     14.3475     1.6180 66.9277   8.868 6.67e-13 ***
## PopulationInyo      7.5720     1.3596 60.8809   5.569 6.13e-07 ***
## PopulationArizona   2.8949     1.1286 54.0655   2.565   0.0131 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) PpltnZ PpltnI
## PopulatinZn -0.542              
## PopulatnIny -0.645  0.349       
## PopultnArzn -0.776  0.421  0.500

ANOVA:

## Type III Analysis of Variance Table with Satterthwaite's method
##            Sum Sq Mean Sq NumDF  DenDF F value    Pr(>F)    
## Population 744.35  248.12     3 61.491  30.819 2.762e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Estimated marginal means & contrasts across populations:

## $emmeans
##  Population emmean    SE   df lower.CL upper.CL
##  Logan        23.8 0.879 54.9     22.1     25.6
##  Zion         38.2 1.362 71.7     35.5     40.9
##  Inyo         31.4 1.041 64.5     29.3     33.5
##  Arizona      26.7 0.713 51.5     25.3     28.2
## 
## Degrees-of-freedom method: kenward-roger 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast        estimate   SE   df t.ratio p.value
##  Logan - Zion      -14.35 1.62 66.4 -8.854  <.0001 
##  Logan - Inyo       -7.57 1.36 60.3 -5.558  <.0001 
##  Logan - Arizona    -2.89 1.13 53.5 -2.558  0.0624 
##  Zion - Inyo         6.78 1.71 69.0  3.953  0.0010 
##  Zion - Arizona     11.45 1.54 66.9  7.451  <.0001 
##  Inyo - Arizona      4.68 1.26 60.0  3.706  0.0025 
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: tukey method for comparing a family of 4 estimates

Interpretation: Zion has longer stamens then all other populations. Inyo has longer stamens than Logan and Arizona. Logan and Arizona have comparable stamens.

Style Length:

Diagnostics for the model residuals:

Model summary:

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: M.Style_Length ~ Population + (1 | Pop_Plant)
##    Data: morph_names
## 
## REML criterion at convergence: 666.9
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.11023 -0.44380 -0.02053  0.39063  2.91571 
## 
## Random effects:
##  Groups    Name        Variance Std.Dev.
##  Pop_Plant (Intercept) 13.83    3.719   
##  Residual              14.11    3.757   
## Number of obs: 113, groups:  Pop_Plant, 63
## 
## Fixed effects:
##                   Estimate Std. Error     df t value Pr(>|t|)    
## (Intercept)         25.629      1.156 50.125  22.178  < 2e-16 ***
## PopulationZion      13.594      2.135 61.865   6.369 2.65e-08 ***
## PopulationInyo       7.516      1.793 55.613   4.191   0.0001 ***
## PopulationArizona    1.211      1.488 48.733   0.814   0.4197    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) PpltnZ PpltnI
## PopulatinZn -0.541              
## PopulatnIny -0.644  0.349       
## PopultnArzn -0.776  0.420  0.500

ANOVA:

## Type III Analysis of Variance Table with Satterthwaite's method
##            Sum Sq Mean Sq NumDF  DenDF F value    Pr(>F)    
## Population  780.9   260.3     3 56.228  18.446 1.869e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Estimated marginal means & contrasts across populations:

## $emmeans
##  Population emmean   SE   df lower.CL upper.CL
##  Logan        25.6 1.16 54.8     23.3     28.0
##  Zion         39.2 1.80 71.8     35.6     42.8
##  Inyo         33.1 1.37 64.5     30.4     35.9
##  Arizona      26.8 0.94 51.4     25.0     28.7
## 
## Degrees-of-freedom method: kenward-roger 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast        estimate   SE   df t.ratio p.value
##  Logan - Zion      -13.59 2.14 66.4 -6.359  <.0001 
##  Logan - Inyo       -7.52 1.80 60.3 -4.182  0.0005 
##  Logan - Arizona    -1.21 1.49 53.4 -0.812  0.8486 
##  Zion - Inyo         6.08 2.26 69.0  2.687  0.0437 
##  Zion - Arizona     12.38 2.03 66.9  6.106  <.0001 
##  Inyo - Arizona      6.30 1.66 60.0  3.787  0.0020 
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: tukey method for comparing a family of 4 estimates

Interpretation: Zion has longer styles then all other populations. Inyo has longer styles than Logan and Arizona. Logan and Arizona have comparable styles.

Hypanthium Length:

Diagnostics for the model residuals:

It looks like there is one outlier: rm2-28 (Arizona) the fifth flower, measured on 6/19. It has a length of 36.48, but the other four flowers from the plant all have lengths over 100. I suspect that the 100 digit may have been dropped from this measurement. Can we either resolve this from the paper datasheet or remove this outlier?

Model summary:

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: M.Hypanthium_Length ~ Population + (1 | Pop_Plant)
##    Data: morph_names
## 
## REML criterion at convergence: 940.7
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -5.9581 -0.4133  0.0357  0.3920  1.9928 
## 
## Random effects:
##  Groups    Name        Variance Std.Dev.
##  Pop_Plant (Intercept)  30.71    5.541  
##  Residual              264.19   16.254  
## Number of obs: 113, groups:  Pop_Plant, 63
## 
## Fixed effects:
##                   Estimate Std. Error     df t value Pr(>|t|)    
## (Intercept)         91.844      3.238 50.519  28.360  < 2e-16 ***
## PopulationZion      29.713      6.414 80.211   4.633 1.38e-05 ***
## PopulationInyo      37.806      5.208 65.042   7.259 6.01e-10 ***
## PopulationArizona   43.706      4.135 47.631  10.571 4.38e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) PpltnZ PpltnI
## PopulatinZn -0.505              
## PopulatnIny -0.622  0.314       
## PopultnArzn -0.783  0.396  0.487

ANOVA:

## Type III Analysis of Variance Table with Satterthwaite's method
##            Sum Sq Mean Sq NumDF  DenDF F value    Pr(>F)    
## Population  31070   10357     3 63.838  39.202 1.732e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Estimated marginal means & contrasts across populations:

## $emmeans
##  Population emmean   SE   df lower.CL upper.CL
##  Logan        91.8 3.28 44.9     85.2     98.4
##  Zion        121.6 5.55 88.3    110.5    132.6
##  Inyo        129.6 4.10 70.8    121.5    137.8
##  Arizona     135.5 2.61 38.1    130.3    140.8
## 
## Degrees-of-freedom method: kenward-roger 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast        estimate   SE   df t.ratio p.value
##  Logan - Zion      -29.71 6.45 75.6  -4.607 0.0001 
##  Logan - Inyo      -37.81 5.25 59.5  -7.199 <.0001 
##  Logan - Arizona   -43.71 4.19 42.1 -10.437 <.0001 
##  Zion - Inyo        -8.09 6.91 82.1  -1.172 0.6461 
##  Zion - Arizona    -13.99 6.14 77.3  -2.281 0.1114 
##  Inyo - Arizona     -5.90 4.86 59.4  -1.214 0.6206 
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: tukey method for comparing a family of 4 estimates

Interpretation: Logan is lower than the other three populations, which are comparable.

Pedicel length:

Note: there are some potential outliers/zeros values that maybe should be NAs in the dataset right now.

Diagnostics for the model residuals:

Model summary:

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: M.Pedicel_Length ~ Population + (1 | Pop_Plant)
##    Data: morph_names
## 
## REML criterion at convergence: 721
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.3082 -0.4655 -0.1300  0.5969  2.5099 
## 
## Random effects:
##  Groups    Name        Variance Std.Dev.
##  Pop_Plant (Intercept) 24.75    4.975   
##  Residual              22.20    4.712   
## Number of obs: 113, groups:  Pop_Plant, 63
## 
## Fixed effects:
##                   Estimate Std. Error     df t value Pr(>|t|)    
## (Intercept)         16.554      1.511 47.372  10.957 1.39e-14 ***
## PopulationZion       2.093      2.780 58.051   0.753 0.454554    
## PopulationInyo      -3.700      2.340 52.341  -1.581 0.119927    
## PopulationArizona   -6.953      1.947 46.092  -3.572 0.000844 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) PpltnZ PpltnI
## PopulatinZn -0.543              
## PopulatnIny -0.646  0.351       
## PopultnArzn -0.776  0.422  0.501

ANOVA:

## Type III Analysis of Variance Table with Satterthwaite's method
##            Sum Sq Mean Sq NumDF  DenDF F value    Pr(>F)    
## Population 421.92  140.64     3 52.944  6.3352 0.0009442 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Estimated marginal means & contrasts across populations:

## $emmeans
##  Population emmean   SE   df lower.CL upper.CL
##  Logan        16.6 1.51 55.3    13.52     19.6
##  Zion         18.6 2.34 70.8    13.99     23.3
##  Inyo         12.9 1.79 64.1     9.28     16.4
##  Arizona       9.6 1.23 52.1     7.13     12.1
## 
## Degrees-of-freedom method: kenward-roger 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast        estimate   SE   df t.ratio p.value
##  Logan - Zion       -2.09 2.78 65.9 -0.752  0.8755 
##  Logan - Inyo        3.70 2.34 60.3  1.578  0.3987 
##  Logan - Arizona     6.95 1.95 54.0  3.564  0.0042 
##  Zion - Inyo         5.79 2.94 68.2  1.968  0.2101 
##  Zion - Arizona      9.05 2.64 66.3  3.426  0.0057 
##  Inyo - Arizona      3.25 2.17 60.0  1.498  0.4452 
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: tukey method for comparing a family of 4 estimates

Interpretation: The only significant contrasts are that Logan and Zion have larger pedicel lengths than Arizona.

Nectar column:

Note: there are some potential outliers/zeros values that maybe should be NAs in the dataset right now.

Diagnostics for the model residuals:

Model summary:

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: M.Nectar_Column ~ Population + (1 | Pop_Plant)
##    Data: morph_names
## 
## REML criterion at convergence: 1187.6
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.7651 -0.5456 -0.0139  0.3381  5.4212 
## 
## Random effects:
##  Groups    Name        Variance Std.Dev.
##  Pop_Plant (Intercept)  249     15.78   
##  Residual              2584     50.84   
## Number of obs: 113, groups:  Pop_Plant, 63
## 
## Fixed effects:
##                   Estimate Std. Error     df t value Pr(>|t|)    
## (Intercept)         30.774      9.949 37.385   3.093  0.00374 ** 
## PopulationZion      49.809     19.794 69.610   2.516  0.01416 *  
## PopulationInyo      43.471     16.038 52.061   2.710  0.00908 ** 
## PopulationArizona   74.193     12.694 34.702   5.845 1.28e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) PpltnZ PpltnI
## PopulatinZn -0.503              
## PopulatnIny -0.620  0.312       
## PopultnArzn -0.784  0.394  0.486

ANOVA:

## Type III Analysis of Variance Table with Satterthwaite's method
##            Sum Sq Mean Sq NumDF  DenDF F value    Pr(>F)    
## Population  88513   29504     3 50.452  11.416 7.922e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Estimated marginal means & contrasts across populations:

## $emmeans
##  Population emmean   SE   df lower.CL upper.CL
##  Logan        30.8 10.1 44.3     10.5     51.1
##  Zion         80.6 17.2 89.2     46.5    114.7
##  Inyo         74.2 12.7 71.2     49.0     99.5
##  Arizona     105.0  8.0 37.2     88.8    121.2
## 
## Degrees-of-freedom method: kenward-roger 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast        estimate   SE   df t.ratio p.value
##  Logan - Zion      -49.81 19.9 76.1 -2.502  0.0676 
##  Logan - Inyo      -43.47 16.2 59.4 -2.687  0.0449 
##  Logan - Arizona   -74.19 12.9 41.4 -5.766  <.0001 
##  Zion - Inyo         6.34 21.3 82.9  0.297  0.9908 
##  Zion - Arizona    -24.38 18.9 78.0 -1.287  0.5737 
##  Inyo - Arizona    -30.72 15.0 59.4 -2.051  0.1812 
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: tukey method for comparing a family of 4 estimates

Interpretation: Logan is lower than Arizona and Inyo.

Percent sugar:

Note: there are some potential outliers/zeros values that maybe should be NAs in the dataset right now.

Diagnostics for the model residuals:

Model summary:

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: M.Percent_Sugar ~ Population + (1 | Pop_Plant)
##    Data: morph_names
## 
## REML criterion at convergence: 700.2
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.1849 -0.2773  0.1092  0.4407  1.8411 
## 
## Random effects:
##  Groups    Name        Variance Std.Dev.
##  Pop_Plant (Intercept)  9.04    3.007   
##  Residual              24.78    4.978   
## Number of obs: 113, groups:  Pop_Plant, 63
## 
## Fixed effects:
##                   Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)        23.2058     1.1812 43.0687  19.645   <2e-16 ***
## PopulationZion      4.7336     2.2560 64.2276   2.098   0.0398 *  
## PopulationInyo      4.0450     1.8640 52.7764   2.170   0.0345 *  
## PopulationArizona   0.9482     1.5148 41.0303   0.626   0.5348    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) PpltnZ PpltnI
## PopulatinZn -0.524              
## PopulatnIny -0.634  0.332       
## PopultnArzn -0.780  0.408  0.494

ANOVA:

## Type III Analysis of Variance Table with Satterthwaite's method
##            Sum Sq Mean Sq NumDF  DenDF F value  Pr(>F)  
## Population 194.09  64.698     3 52.978  2.6105 0.06095 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Anova is not significant.

Multivariate analysis of scent and morphology together

## 
## Call:
## adonis(formula = All_data ~ Population, data = All_data_names,      permutations = 999, method = "bray") 
## 
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##            Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)    
## Population  3    2.1856 0.72855   4.967 0.26656  0.001 ***
## Residuals  41    6.0138 0.14668         0.73344           
## Total      44    8.1994                 1.00000           
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Population explains about 28 % of the variation in percent composition of floral scent and in morphology. (As a reminder, population explained about 23 % of variation in the scent only dataset, and about 39 % of variation in the morphology only dataset.)

Running a constrained analysis of principle coordinates:

## 
## Call:
## capscale(formula = All_data ~ Population, data = All_data_names,      distance = "bray") 
## 
## Partitioning of squared Bray distance:
##               Inertia Proportion
## Total           9.071     1.0000
## Constrained     2.244     0.2474
## Unconstrained   6.827     0.7526
## 
## Eigenvalues, and their contribution to the squared Bray distance 
## 
## Importance of components:
##                         CAP1    CAP2    CAP3   MDS1   MDS2    MDS3   MDS4
## Eigenvalue            1.9963 0.13405 0.11345 2.0705 1.2325 0.84055 0.7430
## Proportion Explained  0.2201 0.01478 0.01251 0.2282 0.1359 0.09266 0.0819
## Cumulative Proportion 0.2201 0.23485 0.24736 0.4756 0.6115 0.70414 0.7860
##                          MDS5    MDS6    MDS7    MDS8    MDS9   MDS10   MDS11
## Eigenvalue            0.54344 0.38177 0.24733 0.15272 0.11559 0.10850 0.09278
## Proportion Explained  0.05991 0.04209 0.02727 0.01684 0.01274 0.01196 0.01023
## Cumulative Proportion 0.84595 0.88804 0.91530 0.93214 0.94488 0.95684 0.96707
##                          MDS12    MDS13    MDS14    MDS15   MDS16   MDS17
## Eigenvalue            0.074755 0.050659 0.044638 0.039513 0.02576 0.02350
## Proportion Explained  0.008241 0.005585 0.004921 0.004356 0.00284 0.00259
## Cumulative Proportion 0.975312 0.980896 0.985817 0.990173 0.99301 0.99560
##                          MDS18    MDS19     MDS20     MDS21     MDS22     MDS23
## Eigenvalue            0.014872 0.009476 0.0080610 0.0044234 0.0023432 7.074e-04
## Proportion Explained  0.001639 0.001045 0.0008886 0.0004876 0.0002583 7.798e-05
## Cumulative Proportion 0.997243 0.998287 0.9991761 0.9996637 0.9999220 1.000e+00
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CAP1    CAP2    CAP3
## Eigenvalue            1.9963 0.13405 0.11345
## Proportion Explained  0.8897 0.05974 0.05056
## Cumulative Proportion 0.8897 0.94944 1.00000
## 
## Scaling 2 for species and site scores
## * Species are scaled proportional to eigenvalues
## * Sites are unscaled: weighted dispersion equal on all dimensions
## * General scaling constant of scores:

The constrained portion explains about 26% of overall distance. CAP1 explains about 24% and CAP2 expalins about 1.5% of overall distance.

Plotting the capscale:

Checking to see which compound group(s) are significantly correlated with CAP1 and/or CAP2.

variables cor1 p1 cor2 p2 sig1 sig2
M.Corolla_D1 0.38 0.0422 -0.1507 0.4844 No No
M.Corolla_D2 0.2573 0.1678 -0.1815 0.4844 No No
M.Tube_Flare 0.1703 0.3871 -0.132 0.5086 No No
M.Stamen_Length 0.306 0.1228 -0.1561 0.4844 No No
M.Style_Length 0.2915 0.1324 -0.2437 0.3737 No No
M.Hypanthium_Length 0.6106 0.0001 0.0407 0.8973 Yes No
M.Pedicel_Length -0.2168 0.2463 -0.0325 0.8973 No No
M.Nectar_Column 0.2682 0.1572 0.0281 0.8973 No No
M.Percent_Sugar 0.1181 0.5433 -0.2299 0.3859 No No
G.ILE 0.458 0.0082 -0.3256 0.2035 Yes No
G.LEU 0.5587 0.0005 -0.4794 0.0091 Yes Yes
G.PHE -0.0748 0.7295 0.1578 0.4844 No No
G.OCI -0.0652 0.7369 0.1696 0.4844 No No
G.GER 0.1658 0.3871 -0.2725 0.2947 No No
G.LIN 0.7372 0.0000 -0.508 0.0077 Yes Yes
G.LOX 0.0076 0.9606 0.0123 0.9359 No No
G.CAR -0.309 0.1228 -0.1856 0.4844 No No
G.FAR -0.0587 0.7369 -0.1405 0.5004 No No
G.SES 0.2861 0.1324 -0.1846 0.4844 No No
G.NER 0.1491 0.4311 -0.2786 0.2947 No No
G.ISO 0.2432 0.1879 -0.0981 0.6444 No No
G.ALT 0.38 0.0422 -0.1507 0.4844 No No

Correlated with CAP 1: Corolla D2 (+), Tube flare (+), Stamen length (+), Style length (+), Hypanthium Length (+), Nectar Column (+), Percent sugar (+), LEU (+), PHE (+), OCI (+), GER (+), LIN (+), CAR (+), FAR (+), NER (+), ISO (+), ALT (+)

Correlated with CAP 2: Hypanthium Length (-), Pedicel Length (+), LIN (-), LOX (+)